CN1321266C - Rotor blade of diagonal flow water turbine - Google Patents

Abstract

The present invention relates to a blade of a rotating wheel for diagonal flow water turbines. The present invention establishes a reasonable flow model, the flow model and basic equations (1), (6), (12) and (14) are used to constitute a main equation for quasi-3D indirect problem calculation based on the S1 stream interface, basic data are obtained according to the design calculation with the basic equations, and a blade of a rotating wheel for diagonal flow water turbines is manufactured according to the basic data. The present invention has good energy and cavitation properties, the rotating wheel has 5 to 6 blades, the present invention is applied to water heads of 30 meters to 70 meters, and the present invention overcomes the defects on the economic aspect and the technical aspect of the applying water head section (30 meters to 70 meters) of a mixed-flow turbine and an axial flow turbine.

Description

Rotor blade of diagonal flow water turbine

Technical field:

The present invention relates to a kind of rotor blade of diagonal flow water turbine, belong to field of fluid machinery.

Background technique:

Water turbine is the spcific power machinery in water power plant, and the electric motor power in water power plant accounts for 25% of national total installation of generating capacity, and therefore, the performance of water turbine is directly connected to exerting oneself of water power plant and life-span.The main pattern of water turbine has axial flow, mixed-flow, tubular, impact type etc., and inclined flow turbine is a kind of type between axial flow and mixed-flow.In the patent documentation data storehouse, as the patent No. be: ZL97195388.0 " impeller of Francis turbine " only proposed structure shape, and do not propose the designing and calculating math equation representation of water turbine rotary impeller, thereby can not set up hydraulic model.

In inclined flow turbine design theory of publishing and method as: (Bankhend water power plant runner is changed design for scheme research/(Canada) HungD; Yin Jihong // " external big motor " .-2001 (4) .-77-81), only told about the three-dimensional computations program that the inclined flow turbine runner is changed scheme and existing runner carried out Transform Type design, with two the relative current foliation opinions of utilizing involved in the present invention, the runner parameter concrete according to the inclined flow turbine runner, set up flow equation, calculate different by the accurate ternary of two stream interface iterative computation.

And for example (Ji // " external big motor " .-1999 (2) .-47-51 is counted in the development/river, palace of the big capacity variable speed of high head diagonal flow type pump turbine), this article adopts the mobile analytical method of several numerals to design the diagonal flow type pump turbine, its working head and I/O power are the twice of conventional unit, and have carried out corresponding model test.Introduced the model test result of this kind pump turbine, viewpoint from hydrodynamics and structural strength, determine that fixed guide vane and movable guide vane are respectively 24, the runner bucket number is 10, rotor blade of diagonal flow water turbine to the effect that of the present invention, the design head section is between 30-70 rice, and the number of blade is 5 or 6, and is all different from the angle of structural type and usage range.

(calculating/the Yu Zhiming of diagonal flow type pump turbine operating mode zero delivery braking moment // " Shenyang Institute of Aeronautical Engineering?'s journal " .-2000 for another example, 17 (3) .-81-83), this article utilizes the static complete characteristic curve of the model of π o-pattern diagonal flow type pump turbine, analyze the principal element that influences pump operating mode zero delivery braking moment, derived the formula of diagonal flow type pump operating condition zero delivery braking moment.The main valve that is applicable to diagonal flow type pump turbine unit is closed, and when stator, wheel blade were opened with certain rule, the pump operating mode was started the calculating of transition, did not also relate to the category of turbine runner blade.

(seriation/Pengze unit // " water power plant mechanical ﹠ electrical technology " .-1994 of small capacity inclined flow turbine in all-electric more and for example, 7 (3) .-65-67), introduced the electronic servomotor of middle small capacity diagonal Kaplan turbine vane operation of Mitsubishi heavy industry and the joint research exploitation of company of Chubu Electric Power, carry out demonstration test by making model machine, finished the seriation of all-electric middle small capacity inclined flow turbine, its main contents are the vane operation control mechanism, compare with inclined flow turbine runner of the present invention and Blade Design, belong to different technical fields.

Summary of the invention:

The objective of the invention is to propose the design method of new inclined flow turbine, according to the relative stream interface (S of two classes according to current actual flow state ₁, S ₂) flow theory and the concrete runner parameter of inclined flow turbine runner, set up the flow equation of two stream interfaces, by the accurate ternary calculation Design of two stream interface iterative computation.Design novel diagonal flow type runner bucket, the runner that makes it to have Reasonable Shape, the water supply power station is selected, and improves the efficient and the anti-cavitation erosion ability of inclined flow turbine.

Design method of the present invention based on the three-dimensional inverse problem calculation of standard with S ₁Stream interface and S _2mStream interface is calculated as the basis, it is characterized in that proposing following flow model, and its design fundamental equation is:

$\frac{\∂}{\∂r}\left(\frac{1}{r{B}_f}\frac{\∂\mathrm{\ψ}}{\∂r}\right)+\frac{\∂}{\∂z}\left(\frac{1}{{\mathrm{rB}}_f}\frac{\∂\mathrm{\ψ}}{\∂z}\right)=\frac{1}{r}(\mathrm{tg\μ}\frac{{\∂V}_{\mathrm{\θ}}r}{\∂r}-\mathrm{tg\λ}\frac{{\∂V}_{\mathrm{\θ}}r}{\∂z})$

$+\frac{1}{W^2}[\frac{\∂E}{\∂r}(W_z-W_{\mathrm{\θ}}\mathrm{tg\μ})-\frac{\∂E}{\∂z}(W_r-W_{\mathrm{\θ}}\mathrm{tg\λ})]---\left(1\right)$

$\frac{\∂}{\∂m}\left(\frac{r}{h}\frac{\∂\mathrm{\Ψ}}{\∂m}\right)+\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{1}{\mathrm{hr}}\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}\right)=2\mathrm{\ωr}\frac{\∂r}{\∂m}=2\sin \mathrm{\σ}---\left(6\right)$

dX/dm＝R ^*/R，dY/dθ＝-R ^* (14)

Symbol illustrates among the mask body embodiment as follows in the above-mentioned formula.

The established angle of described rotor blade of diagonal flow water turbine is between 22.97 °-31.80 ° on the water inlet limit, and going out the waterside is 22.56 °-30.64 °.

Described rotor blade of diagonal flow water turbine number is 5 or 6.

Description of drawings:

The present invention will be further described in conjunction with the accompanying drawings

Fig. 1 runner channel schematic representation

Fig. 2 equivalent speed triangle

Fig. 3 A S ₁Stream interface blade profile unfolded drawing (5 sections)

Fig. 3 B, 3C blade graphics

Fig. 4 A diagonal flow type rotaring wheel structure front view

Fig. 4 B diagonal flow type rotaring wheel structure sectional drawing

Fig. 4 C diagonal flow type runner bucket is installed

Fig. 4 D diagonal flow type runner bucket mounting hole

Fig. 5 A 5 blade rotary wheel pictorial diagram

Fig. 5 B6 blade rotary wheel pictorial diagram

1 diagonal flow type runner bucket molded lines, 2 diagonal flow type runner buckets are closing bolt

3 diagonal flow type webs, 4 keyways, 5 blade positioning pin holes

Embodiment:

Use equation (1), (6), (12), (14) to constitute as shown in Figure 1 and Figure 2 based on S ₁The master equation of the accurate three-dimensional inverse problem calculation of stream interface is passed through S _2mStream interface calculates the S of given initial blade profile ₁Stream interface indirect problem and average S _2mStream interface direct problem iteration, and at turning surface (S ₁Relative stream interface) introduces " equivalent speed triangle ", come the inclination of modifying factor stream interface and axial velocity variation and cause the influence that cascade performance changes, design diagonal flow type runner bucket with axial velocity variation rate ξ and stream interface tilt parameters η.Carry out axial plane and flow and to calculate after axial plane flows, just can obtain some revolution S ₁Face is then at revolution S ₁Design blade shape on the stream interface, by formula at last with these blades

Integration forms the 3D solid blade, and by formula Thickening.Its blade angle is between 22.97 " 31.80 " on the water inlet limit, and going out the waterside is 22.56 " 30.64 ".The number of blade is 5 or 6.

Design-calculated elementary process:

1 based on S ₁The accurate three-dimensional inverse problem calculation mathematical model of stream interface

(1) average S _2mStream interface FLOW CONTROL equation

Suppose that runner inside is mobile relatively permanent, current are inviscid can not press, and actual Three-dimensional Flow in the runner is carried out circumferential average treatment, can get circumferentially average stream function governing equation of runner district:

$\frac{\∂}{\∂r}\left(\frac{1}{{\mathrm{rB}}_f}\frac{\∂\mathrm{\ψ}}{\∂r}\right)+\frac{\∂}{\∂z}\left(\frac{1}{{\mathrm{rB}}_f}\frac{\∂\mathrm{\ψ}}{\∂z}\right)=\frac{1}{r}(\mathrm{tg\μ}\frac{{\∂V}_{\mathrm{\θ}}r}{\∂r}-\mathrm{tg\λ}\frac{{\∂V}_{\mathrm{\θ}}r}{\∂z})$

$+\frac{1}{W^2}[\frac{\∂E}{\∂r}(W_z-W_{\mathrm{\θ}}\mathrm{tg\μ})-\frac{\∂E}{\∂z}(W_r-W_{\mathrm{\θ}}\mathrm{tg\λ})---\left(1\right)$

The average flow function definition is:

$\frac{\∂\mathrm{\ψ}}{\∂r}={\mathrm{rB}}_f\stackrel{\‾}{W_2},\frac{\∂\mathrm{\ψ}}{\∂z}=-{\mathrm{rB}}_f\stackrel{\‾}{W_r}---\left(2\right)$

In the formula: $B_f=\frac{B\·\mathrm{\Δ\θ}}{2\mathrm{\π}}$

Have potential barrier moving for axial plane, tg λ and tg μ are 0, and E is a constant, and therefore, the right-hand vector of equation (1) is 0.

(2) S ₁The relative current surface current moves governing equation

S ₁The continuity equation that turns round on the relative stream interface is:

$\frac{\∂}{\∂m}\left({\mathrm{hrW}}_m\right)+\frac{\∂}{\∂\mathrm{\θ}}\left({\mathrm{hW}}_{\mathrm{\θ}}\right)=0---\left(3\right)$

S ₁The motion equation of stream interface is:

$\frac{\∂\left({\mathrm{rW}}_0\right)}{\∂m}-\frac{{\∂W}_m}{\∂\mathrm{\θ}}=\frac{\∂}{\∂m}\left(k_m\frac{\∂\mathrm{\ψ}}{\∂m}\right)+\frac{\∂}{\∂\mathrm{\θ}}\left(k_{\mathrm{\θ}}\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}\right)---\left(4\right)$

$=2\mathrm{\ωr}\frac{\∂r}{\∂m}=2\mathrm{\ω}r\sin \mathrm{\σ}+\frac{h}{W^2}(\frac{\∂E}{r\∂\mathrm{\θ}}{W}_m-\frac{\∂E}{\∂m}{W}_{\mathrm{\θ}})$

In the formula: $k_m=\frac{r}{h},k_{\mathrm{\θ}}=\frac{1}{\mathrm{hr}}$

H---S ₁The fluid layer thickness of stream interface;

M---meridian plane coordinate.

Equation (3) and (4) have constituted S ₁The fundamental equation group of the relative absolute irrotational motion of stream interface.

According to continuity equation (3) definition stream function be:

$\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}={\mathrm{rhW}}_m,\frac{\∂\mathrm{\ψ}}{\∂m}=-{\mathrm{hW}}_0---\left(5\right)$

Substitution equation (4) can draw S ₁The stream function equation of stream interface relative movement:

$\frac{\∂}{\∂m}\left(\frac{r}{h}\frac{\∂\mathrm{\ψ}}{\∂m}\right)+\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{1}{\mathrm{hr}}\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}\right)=2\mathrm{\ωr}\frac{\∂r}{\∂m}=2\sin \mathrm{\σ}---\left(6\right)$

(3) based on S ₁The blade profile design of stream interface

The blade equation is as follows:

For S ₁Stream interface flows, and is defined as follows circumferentially average:

$\stackrel{\‾}{q}\left(m\right)=\frac{1}{{\mathrm{\θ}}_p-{\mathrm{\θ}}_s}{\∫}_{{\mathrm{\θ}}_s}^{{\mathrm{\θ}}_p}q(m,\mathrm{\θ})\mathrm{d\θ}---\left(8\right)$

Can be with formula (8) introduction-type (7) based on S ₁The blade integral equation that stream interface calculates

In the formula: $\stackrel{\‾}{V_{\mathrm{\θ}}}\left(m\right)=\frac{1}{{\mathrm{\θ}}_p-{\mathrm{\θ}}_s}{\∫}_{{\mathrm{\θ}}_x}^{{\mathrm{\θ}}_p}{V}_{\mathrm{\θ}}(m,\mathrm{\θ})\mathrm{d\θ},$

$\stackrel{\‾}{W_{\mathrm{\θ}}}\left(m\right)=\frac{1}{{\mathrm{\θ}}_p-{\mathrm{\θ}}_s}{\∫}_{{\mathrm{\θ}}_x}^{{\mathrm{\θ}}_p}{W}_{\mathrm{\θ}}(m,\mathrm{\θ})\mathrm{d\θ}$

One first-order ordinary differential equation (9) is found the solution needs given initial condition.Claim that this condition is a blade stack condition, to the inclined flow turbine runner, gets Z _StBe the axial coordinate of blade running shaft, given following initial condition:

(r，z＝z _st)＝0 (10)

Correction formula between initial blade profile and final design blade profile:

Because With  ⁽ⁿ⁾Between be non-linear relation, so adopt relaxative iteration, the blade profile correction can be written as:

Like this, based on given initial blade profile, pass through S _2mStream interface flows and S ₁Stream interface flows and calculates, and employing formula (11) is carried out the correction of blade profile iteration, and makes it to satisfy blade stack condition, has realized S ₁Blade profile design on the stream interface.

Give fixed blade to thickness t _n(r, z θ), consider the three-dimensional twisted of blade, the circumferential thickness t of blade _n(r, z θ) are then provided by following formula:

Based on face in the designed blade, try to achieve thickness t by formula (13) _sCarry out back side thickening, then can obtain the blade of design thickness, realize the accurate three dimensional design of runner.

The conversion of 2 any tilting rotary table stream interfaces

(1) fundamental equation of any tilting rotary table face

Continuity equation:

$\frac{\∂}{\∂m}\left(\mathrm{hr}{W}_m\right)+\frac{\∂}{\∂\mathrm{\θ}}\left({\mathrm{hW}}_{\mathrm{\θ}}\right)=0$

The equation of stream function ψ:

$\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}={\mathrm{rhW}}_m,\frac{\∂\mathrm{\ψ}}{\∂m}=-{\mathrm{hW}}_0$

Be satisfied with the revolution stream interface Equation of Relative Motion with Small of stream function ψ:

$\frac{{\∂}^2\mathrm{\ψ}}{{\∂m}^2}+\frac{1}{r^2}\frac{{\∂}^2\mathrm{\ψ}}{{\∂\mathrm{\θ}}^2}+[\frac{1}{r}\frac{\∂r}{\∂m}-\frac{1}{h}\frac{\∂\left(h\right)}{\∂m}]\frac{\∂\mathrm{\ψ}}{\∂m}-\frac{1}{h}\frac{\∂\left(h\right)}{r\∂\mathrm{\θ}}=2\mathrm{\ωh}\frac{\∂r}{\∂m}$

(2) equivalent speed triangle theory

Decide the benchmark radius R with the revolution stream interface that tilts is in office ^*The developed surface x-y face interior mapping of cylndrical surface.Introduce the map function

dX/dm＝R ^*/R， dY/dθ＝-R ^* (14)

Because the axial velocity of leaf grating inlet/outlet does not wait, therefore introduce " equivalent speed triangle " as shown in Figure 2.

Because of stream interface inclination and axial velocity variation cause the influence that cascade performance changes, reflect with axial velocity variation rate ξ and stream interface tilt parameters η respectively:

$\mathrm{\ξ}=\frac{W_{X2}-W_{X2}}{W_{X\∞}}---\left(15\right)$

$\mathrm{\η}=\frac{{2u}^{*}}{W_{X1}+W_{X2}}\left(\frac{R_1^2-R_2^2}{R^{*2}}\right)---\left(16\right)$

At last, passing through type (14) is transformed into leaf grating on the physical surface.

3 liang of accurate ternary iteration of class stream interface

Equation (1), (6), (12), (14) have constituted based on S ₁The master equation of the accurate three-dimensional inverse problem calculation of stream interface is as follows respectively:

$\frac{\∂}{\∂r}\left(\frac{1}{{\mathrm{rB}}_f}\frac{\∂\mathrm{\ψ}}{\∂r}\right)+\frac{\∂}{\∂z}\left(\frac{1}{{\mathrm{rB}}_f}\frac{\∂\mathrm{\ψ}}{\∂z}\right)=\frac{1}{r}(\mathrm{tg\μ}\frac{{\∂V}_{\mathrm{\θ}}r}{\∂r}-\mathrm{tg\λ}\frac{{\∂V}_{\mathrm{\θ}}r}{\∂z})---\left(1\right)$

$+\frac{1}{W^2}[\frac{\∂E}{\∂r}(W_z-W_{\mathrm{\θ}}\mathrm{tg\μ})-\frac{\∂E}{\∂z}(W_r-W_{\mathrm{\θ}}\mathrm{tg\λ})]$

$\frac{\∂}{\∂m}\left(\frac{r}{h}\frac{\∂\mathrm{\ψ}}{\∂m}\right)+\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{1}{\mathrm{hr}}\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}\right)=2\mathrm{\ωr}\frac{\∂r}{\∂m}=2\sin \mathrm{\σ}---\left(6\right)$

dX/dm＝R ^*/R，dY/dθ＝-R ^* (14)

Equation (1) and equation (6) are set up the finite element equation row iteration of going forward side by side respectively calculate, at S ₁When stream interface calculates, be transformed into the reflection face with equation (14), introduce by " equivalent speed triangle ", come the inclination of modifying factor stream interface and axial velocity variation and cause the influence that cascade performance changes with axial velocity variation rate ξ and stream interface tilt parameters η, use (14) to transform back physical surface again, continue iteration, until satisfying the condition of convergence.

Advantage of the present invention is:

By the research to inclined flow turbine, adopt system, consider the impact between each characteristic of hydraulic turbine performance indications and geometric parameter, use method for designing and the optimum theory of inclined flow turbine, set up Mathematical Modeling, utilize accurate Three Yuan theory, by to S₁/S ₂Stream interface carries out iterative computation, has designed to have the oblique of good hydraulic performance The flow water turbine runner. This inclined flow turbine has improved axial flow hydraulic turbine high water head (more than 30 meters) and mixed flow The flow energy conversion efficiency is low between formula hydraulic turbine low water head (30-70 rice) section, and efficient is low during variable load operation, sky Erosion destroys serious, and the defectives such as power station deficiency in economic performance make this head section (30-70 rice) have the Hydropower Station technological transformation now Or the cost performance of newly building a power station obtains bigger raising.

Claims (3)

1, a kind of rotor blade of diagonal flow water turbine is characterized in that proposing following flow model, and its design fundamental equation is:

$\frac{\∂}{\∂r}\left(\frac{1}{r{B}_f}\frac{\∂\mathrm{\ψ}}{\∂r}\right)+\frac{\∂}{\∂z}\left(\frac{1}{r{B}_f}\frac{\∂\mathrm{\ψ}}{\∂z}\right)=\frac{1}{r}(\mathrm{tg\μ}\frac{\∂V_{\mathrm{\θ}}r}{\∂r}-\mathrm{tg\λ}\frac{\∂V_{\mathrm{\θ}}r}{\∂z})$

$+\frac{1}{W^2}[\frac{\∂E}{\∂r}(W_Z-W_{\mathrm{\θ}}\mathrm{tg\μ})-\frac{\∂E}{\∂z}(W_r-W_{\mathrm{\θ}}\mathrm{th\λ})]---\left(1\right)$

This equation is a circumferentially average stream function governing equation of runner district, in the formula: z, r, θ are cylindrical-coordinate system, W is a relative velocity, W _rBe relative velocity component radially, W _θFor relative velocity along circumferential component, W _zBe relative velocity component vertically; E is the energy of unit mass fluid in the relative movement; $B_f=\frac{\mathrm{B\Δ\θ}}{2\mathrm{\π}};$ ψ is a stream function; Tg λ and tg μ describe the geometrical property of stream interface, by $\mathrm{tg\λ}=\frac{n_r}{n_{\mathrm{\θ}}},$ $\mathrm{tg\μ}=\frac{n_z}{n_{\mathrm{\θ}}}$ Determine n _r, n _θ, n _zRepresent stream interface respectively radially, the unit vector of circumferential and axial;

$\frac{\∂}{\∂m}\left(\frac{r}{h}\frac{\∂\mathrm{\ψ}}{\∂m}\right)+\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{1}{\mathrm{hr}}\frac{\∂\mathrm{\ψ}}{\∂\mathrm{\θ}}\right)=2\mathrm{\ωr}\frac{\∂r}{\∂m}=2\mathrm{\ω}r\sin \mathrm{\σ}---\left(6\right)$

This equation is S ₁The stream function equation of stream interface relative movement, in the formula: r is for calculating streamline place radius, and m is the meridian plane coordinate, and h is S ₁The fluid layer thickness of stream interface, ω are angular velocity, $\sin \mathrm{\σ}=\frac{\∂r}{\∂m}$ Be about S ₁The geometric shape parameters of stream interface is by average S _2mThe mobile calculating of stream interface is given;

This equation is the blade profile update equation, in the formula: r _cFor calculating averaging of income runner radius, r _gBe given mean radius, n is an iterations;

dX/dm＝R ^*/R，dY/dθ＝-R ^* (14)

This equation is the map functional equation, and in the formula: to be that the revolution stream interface that will tilt is in office decide the benchmark radius for X, Y

R ^*The cylinder developed surface on the x-y coordinate, R is a tilting rotary table stream interface radius.

2, rotor blade of diagonal flow water turbine according to claim 1 is characterized in that the established angle of runner bucket is between 22.97 °-31.80 ° on the water inlet limit, and going out the waterside is 22.56 °-30.64 °.

3, rotor blade of diagonal flow water turbine according to claim 1 is characterized in that the runner bucket number is 5 or 6.

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